Question

The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula M=2/3log(E/10^11.8). Find the energy released by an earthquake of magnitude 4.2

Answer 1

To find the energy released by a 4.2 magnitude earthquake, we rearranged the formula to solve for energy (E), and then we substituted 4.2 as the magnitude (M). After performing the calculations we found that the energy released is 10^18.1 ergs.

Step-by-step explanation:

The student is asking to find the energy released by an earthquake with a Richter scale magnitude of 4.2. The formula that relates the Richter magnitude (M) of an earthquake to the energy released in ergs (E) is M = 2/3 log(E/10^11.8).

To solve for E, we rearrange the formula:

1. First, multiply both sides by 3/2 to isolate the logarithmic expression: 3/2 M = log(E/10^11.8).
2. Then, raise 10 to the power of both sides to remove the logarithm: 10^(3/2 M) = E/10^11.8.
3. Next, multiply both sides by 10^11.8 to solve for E: E = 10^11.8 * 10^(3/2 M).
4. Substitute 4.2 for M and calculate E: E = 10^11.8 * 10^(3/2 * 4.2).

To calculate, E = 10^11.8 * 10^(6.3) = 10^18.1 ergs. Therefore, the energy released by a 4.2 magnitude earthquake is 10^18.1 ergs.

Answer 2

4.2 = [2/3] log [E / 10^11.8 ]

4.2 * 3 / 2 = log E - log (10^11.8)

6.3 + 11.8 = log E

18.1 = log E

E = 10^18.1 erg.